| Title:
|
The geography of simply-connected symplectic manifolds (English) |
| Author:
|
Cho, Mi Sung |
| Author:
|
Cho, Yong Seung |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
265-276 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By using the Seiberg-Witten invariant we show that the region under the Noether line in the lattice domain $\mathbb{Z}\times \mathbb{Z}$ is covered by minimal, simply connected, symplectic 4-manifolds. (English) |
| Keyword:
|
Seiberg-Witten invariant |
| Keyword:
|
geography of symplectic 4-manifold |
| MSC:
|
37J99 |
| MSC:
|
53D05 |
| MSC:
|
53D35 |
| MSC:
|
57N13 |
| MSC:
|
57R17 |
| MSC:
|
57R57 |
| MSC:
|
58F05 |
| idZBL:
|
Zbl 1039.53097 |
| idMR:
|
MR1983450 |
| . |
| Date available:
|
2009-09-24T11:01:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127798 |
| . |
| Reference:
|
[1] D. Auckly: Surgery, knots and the Seiberg-Witten equations.Preprint. |
| Reference:
|
[2] D. Auckly: Homotopy K3 surfaces and gluing results in Seiberg-Witten theory.Preprint. Zbl 0870.57022, MR 1437600 |
| Reference:
|
[3] W. Barth, C. Peter and A. Van de Ven: Compact Complex Surfaces. Ergebnisse der Mathematik.Springer-Verlag, Berlin, 1984. MR 0749574 |
| Reference:
|
[4] M. S. Cho and Y. S. Cho: Genus minimizing in symplectic 4-manifolds.Chinese Ann. Math. Ser. B 21 (2000), 115–120. MR 1762280, 10.1142/S0252959900000157 |
| Reference:
|
[5] Y. S. Cho: Finite group actions on the moduli space of self-dual connections I.Trans. Amer. Math. Soc. 323 (1991), 233–261. Zbl 0724.57013, MR 1010409, 10.1090/S0002-9947-1991-1010409-2 |
| Reference:
|
[6] Y. S. Cho: Cyclic group actions in gauge theory.Differential Geom. Appl. 6 (1996), 87–99. MR 1384881, 10.1016/0926-2245(96)00009-5 |
| Reference:
|
[7] Y. S. Cho: Seiberg-Witten invariants on non-symplectic 4-manifolds.Osaka J. Math. 34 (1997), 169–173. Zbl 0882.57013, MR 1439004 |
| Reference:
|
[8] Y. S. Cho: Finite group actions and Gromov-Witten invariants.Preprint. |
| Reference:
|
[9] R. Fintushel and R. Stern: Surgery in cusp neighborhoods and the geography of Irreducible 4-manifolds.Invent. Math. 117 (1994), 455–523. MR 1283727, 10.1007/BF01232253 |
| Reference:
|
[10] R. Fintushel and R. Stern: Rational blowdowns of smooth 4-manifolds.Preprint. MR 1484044 |
| Reference:
|
[11] R. Gompf: A new construction of symplectic manifolds.Ann. Math. 142 (1995), 527–595. Zbl 0849.53027, MR 1356781, 10.2307/2118554 |
| Reference:
|
[12] P. Kronheimer and T. Mrowka: The genus of embedded surfaces in the projective plane.Math. Res. Lett. (1994), 794–808. MR 1306022 |
| Reference:
|
[13] U. Persson: Chern invariants of surfaces of general type.Composito Math. 43 (1981), 3–58. Zbl 0479.14018, MR 0631426 |
| Reference:
|
[14] D. Salamon: Spin geometry and Seiberg-Witten invariants.University of Warwick (1995). |
| Reference:
|
[15] A. Stipsicz: A note on the geography of symplectic manifolds.Preprint. Zbl 0876.57039 |
| Reference:
|
[16] C. H. Taubes: The Seiberg-Witten invariants and symplectic forms.Math. Res. Lett. 1 (1994), 809–822. Zbl 0853.57019, MR 1306023, 10.4310/MRL.1994.v1.n6.a15 |
| . |
